arXiv subjects

Fabian Müller

Publications and source records attributed to Fabian Müller.

At least 19 recordsLinked to original sources

arXiv2026

Connecting Quantum Tomography and Quantum Retrodiction

Quantum tomography and quantum retrodiction are traditionally viewed as separate inference tasks: tomography reconstructs quantum states from measurement data, whereas retrodiction infers past quantum states from observed outcomes. We show that the two are manifestations of the same underlying principle. We prove that the Petz recovery map associated with a measurement channel is precisely the gradient update of the log-likelihood used in maximum-likelihood tomography. Consequently, repeated applications of the Petz map monotonically increase the likelihood. Extending beyond measurement channels, we derive a noncommutative generalization of the Petz map from the gradient of a generalized likelihood for arbitrary quantum channels. The resulting iterative procedure maximizes the likelihood and provides a general framework for quantum tomography, establishing a direct bridge between retrodiction, recovery maps, and statistical inference.

quant-ph↗

arXiv2026

Rotational Quantum Tunneling of a Magnetic Dipole in a Superconducting Trap

We study the quantum dynamics of the rotational degree of freedom of a nano-magnet trapped in a superconducting trap. The nano-magnet is modeled as a magnetic dipole with magnetization pinned to the easy axis of the particle. The magnetic trap then leads to a potential barrier that hinders free rotation of the particle, but through which it can tunnel. We identified rest-gas scattering as the most important decoherence mechanism at low temperatures. A shape of the particle sufficiently close to perfect rotational symmetry about the rotational axis can protect the rotational tunneling against this decoherence mechanism, and we identify experimentally feasible parameter regimes where rotational tunneling should be observable.

quant-ph↗

arXiv2025

Interferometric Mass Photometry at the Quantum Limit of Sensitivity

We present an innovative optical imaging system for measuring parameters of a small particle such as a macromolecule or nanoparticle at the quantum limit of sensitivity. In comparison to the conventional confocal interferometric scattering (iSCAT) approach, our setup adds a second arm to form a Michelson interferometer that allows us to tune a relative phase. We evaluate the quantum Cramér-Rao bound (QCRB) for different quantum states, including single-mode coherent states, multi-frequency coherent states, and phase-averaged coherent states. Our results show that the proposed setup can achieve the QCRB of sensitivity and outperform iSCAT for all considered quantum states for mass and phase estimation of a particle.

quant-ph↗

arXiv2024

Finite-volume effects in the $δ$-regime

We derive a systematic perturbative expansion for the finite-volume energy spectrum of the non-linear $O(N)$ $σ$-model in the $δ$-regime. The violation of the power-counting rules that emerges after the separation of the fast and slow modes is dealt with to all orders by use of the threshold expansion. The known result for the rest-frame energy spectrum up-to-and-including next-to-next-to-leading order is reproduced.

hep-lat↗

arXiv2024

Lellouch-Lüscher factor for the $K\to 3π$ decays

We derive an explicit expression for the Lellouch-Lüscher (LL) factor in the $K\to 3π$ decays at leading order (without derivative couplings). Several important technical details are addressed, like a proper decomposition into the isospin amplitudes, the choice of a minimal set of effective couplings and the renormalization, as well as the algorithm for the solution of the pertinent Faddeev equations in the infinite volume which is based on the contour deformation method. Most importantly, our numerical results demonstrate that the three-body force contributes very little to the LL factor. This result paves the way for the study of the $K\to 3π$ decays on the lattice.

hep-lat↗

arXiv2024

Lüscher equation with long-range forces

We derive the modified Lüscher equation in the presence of the long-range force caused by the exchange of a light particle. It is shown that the use of this equation enables one to circumvent the problems related to the strong partial-wave mixing and the t-channel sub-threshold singularities. It is also demonstrated that the present method is intrinsically linked to the so-called modified effective-range expansion (MERE) in the infinite volume. A detailed comparison with the two recently proposed alternative approaches is provided.

hep-lat↗

arXiv2023

First Search for Axion-Like Particles in a Storage Ring Using a Polarized Deuteron Beam

Based on the notion that the local dark-matter field of axions or axion-like particles (ALPs) in our Galaxy induces oscillating couplings to the spins of nucleons and nuclei (via the electric dipole moment of the latter and/or the paramagnetic axion-wind effect), we establish the feasibility of a new method to search for ALPs in storage rings. Based on previous work that allows us to maintain the in-plane polarization of a stored deuteron beam for a few hundred seconds, we performed a first proof-of-principle experiment at the Cooler Synchrotron COSY to scan momenta near 970 MeV/c. This entailed a scan of the spin precession frequency. At resonance between the spin precession frequency of deuterons and the ALP-induced EDM oscillation frequency there will be an accumulation of the polarization component out of the ring plane. Since the axion frequency is unknown, the momentum of the beam and consequently the spin precession frequency were ramped to search for a vertical polarization change that would occur when the resonance is crossed. At COSY, four beam bunches with different polarization directions were used to make sure that no resonance was missed because of the unknown relative phase between the polarization precession and the axion/ALP field. A frequency window of 1.5-kHz width around the spin precession frequency of 121 kHz was scanned. We describe the experimental procedure and a test of the methodology with the help of a radiofrequency Wien filter located on the COSY ring. No ALP resonance was observed. As a consequence an upper limit of the oscillating EDM component of the deuteron as well as its axion coupling constants are provided.

hep-ex↗

arXiv2023

Finite-volume energy shift of the three-nucleon ground state

A perturbative calculation of the three-nucleon ground-state energy shift in a finite volume is carried out within the non-relativistic effective theory. The energy shift is evaluated up to and including $\mathcal{O}(L^{-6})$, where $L$ is the size of a cubic box. The convergence of the perturbative series at physical values of the scattering lengths is studied numerically.

hep-lat↗

arXiv2023

Three-particle Lellouch-Lüscher formalism in moving frames

A manifestly relativistic-invariant Lellouch-Lüscher formalism for the three-particle decays is proposed. Similarly to ref.[1], the formalism is based on the use of the non-relativistic effective Lagrangians. Manifest Lorentz invariance is guaranteed, as in ref.[2], by choosing the quantization axis along the total four-momentum of the three-particle system. A systematic inclusion of the higher-order derivative couplings, as well as higher partial waves is addressed.

hep-lat↗

arXiv2022

Phononic heat conductance of gold atomic contacts: Coherent versus incoherent transport

We present here a theoretical method to determine the phononic contribution to the thermal conductance of nanoscale systems in the phase-coherent regime. Our approach makes use of classical molecular dynamics (MD) simulations to calculate the temperature-dependent dynamical matrix, and the phononic heat conductance is subsequently computed within the Landauer-Büttiker formalism with the help of nonequilibrium Green's function techniques. Tailored to nanostructures, crucial steps of force constant and heat transport calculations are performed directly in real space. As compared to conventional density functional theory (DFT) approaches, the advantage of our method is two-fold. First, interatomic interactions can be described with the method of choice. Semiempirical potentials may lead to large computational speedups, enabling the study of much larger systems. Second, the method naturally takes into account the temperature dependence of atomic force constants, an aspect that is ignored in typical static DFT-based calculations. We illustrate our method by analyzing the temperature dependence of the phononic thermal conductance of gold (Au) chains with lengths ranging from 1 to 12 atoms. Moreover, in order to evaluate the importance of anharmonic effects in these atomic-scale wires, we compare the phase-coherent approach with nonequilibrium MD (NEMD) simulations. We find that the predictions of the phase-coherent method and the classical NEMD approach largely agree above the Debye temperature for all studied chain lengths, which shows that heat transport is coherent and that our phase-coherent approach is well suited for such nanostructures.

cond-mat.mes-hall↗

arXiv2022

Spurious poles in a finite volume

Using effective-range expansion for the two-body amplitudes may generate spurious sub-threshold poles outside of the convergence range of the expansion. In the infinite volume, the emergence of such poles leads to the inconsistencies in the three-body equations, e.g., to the breakdown of unitarity. We investigate the effect of the spurious poles on the three-body quantization condition in a finite volume and show that it leads to a peculiar dependence of the energy levels on the box size $L$. Furthermore, within a simple model, it is demonstrated that the procedure for the removal of these poles, which was recently proposed in Ref.[1] in the infinite volume, can be adapted to the finite-volume calculations. The structure of the exact energy levels is reproduced with an accuracy that systematically improves order by order in the EFT expansion.

hep-lat↗

arXiv2022

Relativistic-invariant formulation of the NREFT three-particle quantization condition

A three-particle quantization condition on the lattice is written down in a manifestly relativistic-invariant form by using a generalization of the non-relativistic effective field theory (NREFT) approach. Inclusion of the higher partial waves is explicitly addressed. A partial diagonalization of the quantization condition into the various irreducible representations of the (little groups of the) octahedral group has been carried out both in the center-of-mass frame and in moving frames. Furthermore, producing synthetic data in a toy model, the relativistic invariance is explicitly demonstrated for the three-body bound state spectrum.

hep-lat↗

arXiv2021

Finite-volume energy shift of the three-pion ground state

Using the framework of non-relativistic effective field theory, the finite-volume ground-state energy shift is calculated up-to-and-including $O(L^{-6})$ for the system of three pions in the channel with the total isospin $I=1$. The relativistic corrections are included perturbatively, up to the same order in the inverse of the box size $L$. The obtained explicit expression, together with the known result for the system with maximal isospin $I=3$, can be used for the extraction of two independent effective three-body couplings from the measured ground-state spectrum of three pions.

hep-lat↗

arXiv2021

On the three-particle analog of the Lellouch-Lüscher formula

Using non-relativistic effective field theory, we derive a three-particle analog of the Lellouch-Lüscher formula at the leading order. This formula relates the three-particle decay amplitudes in a finite volume with their infinite-volume counterparts and, hence, can be used to study the three-particle decays on the lattice. The generalization of the approach to higher orders is briefly discussed.

hep-lat↗

arXiv2020

Counting of Teams in First-Order Team Logics

We study descriptive complexity of counting complexity classes in the range from #P to #$\cdot$NP. A corollary of Fagin's characterization of NP by existential second-order logic is that #P can be logically described as the class of functions counting satisfying assignments to free relation variables in first-order formulae. In this paper we extend this study to classes beyond #P and extensions of first-order logic with team semantics. These team-based logics are closely related to existential second-order logic and its fragments, hence our results also shed light on the complexity of counting for extensions of FO in Tarski's semantics. Our results show that the class #$\cdot$NP can be logically characterized by independence logic and existential second-order logic, whereas dependence logic and inclusion logic give rise to subclasses of #$\cdot$NP and #P , respectively. Our main technical result shows that the problem of counting satisfying assignments for monotone Boolean $Σ_1$-formulae is #$\cdot$NP-complete as well as complete for the function class generated by dependence logic.

cs.LO↗

arXiv2020

Enumerating Teams in First-Order Team Logics

We start the study of the enumeration complexity of different satisfiability problems in first-order team logics. Since many of our problems go beyond DelP, we use a framework for hard enumeration analogous to the polynomial hierarchy, which was recently introduced by Creignou et al. (Discret. Appl. Math. 2019). We show that the problem to enumerate all satisfying teams of a fixed formula in a given first-order structure is DelNP-complete for certain formulas of dependence logic and independence logic. For inclusion logic formulas, this problem is even in DelP. Furthermore, we study the variants of this problems where only maximal, minimal, maximum and minimum solutions, respectively, are considered. For the most part these share the same complexity as the original problem. An exception is the minimum-variant for inclusion logic, which is DelNP-complete.

cs.LO↗

arXiv2020

Systematic Analysis of the Sensor Coverage of Automated Vehicles Using Phenomenological Sensor Models

The objective of this paper is to propose a systematic analysis of the sensor coverage of automated vehicles. Due to an unlimited number of possible traffic situations, a selection of scenarios to be tested must be applied in the safety assessment of automated vehicles. This paper describes how phenomenological sensor models can be used to identify system-specific relevant scenarios. In automated driving, the following sensors are predominantly used: camera, ultrasonic, \radar and \lidarohne. Based on the literature, phenomenological models have been developed for the four sensor types, which take into account phenomena such as environmental influences, sensor properties and the type of object to be detected. These phenomenological models have a significantly higher reliability than simple ideal sensor models and require lower computing costs than realistic physical sensor models, which represents an optimal compromise for systematic investigations of sensor coverage. The simulations showed significant differences between different system configurations and thus support the system-specific selection of relevant scenarios for the safety assessment of automated vehicles.

cs.RO↗

arXiv2019

Extraction of Azimuthal Asymmetries using Optimal Observables

Azimuthal asymmetries play an important role in scattering processes with polarized particles. This paper introduces a new procedure using event weighting to extract these asymmetries. It is shown that the resulting estimator has several advantages in terms of statistical accuracy, bias, assumptions on acceptance and luminosities compared to other estimators discussed in the literature.

physics.data-an↗